Multidimensional Lines. I: Representation

Based on a system of parallel coordinates, a methodology for visualizing multivariate relations (i.e., subsets of RN) by mapping them uniquely into indexed subsets of R² was introduced earlier. Here, the foundations for the representation mapping in general are given, and the representation of lines in RN by $N - 1$ planar points indexed by a pair of distinct integers from \ 0,1,2, ⋯ ,N \ in R² is obtained. This yields construction and display algorithms for the representation of lines, points on lines, changes of parameterization, and line transformations.